Journal
ADVANCES IN DIFFERENCE EQUATIONS
Volume -, Issue -, Pages -Publisher
SPRINGER INTERNATIONAL PUBLISHING AG
DOI: 10.1186/s13662-015-0729-7
Keywords
singular fractional differential equation; integral boundary conditions; positive solution; Green function; Leray-Schauder nonlinear alternative
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In this paper, we discuss the existence and multiplicity of positive solutions for singular fractional differential equations with integral boundary value conditions {CD(alpha)u(t) + f(t, u(t)) = 0, 0 < t < 1, u ''(0) = u''' (0) = 0, u '(0) = u(1) = eta integral(1)(0) u(s) ds, where 3 < alpha < 4, 0 < eta < 2, D-C(alpha) is the Caputo fractional derivative and f may be singular at u = 0. Our results are based on the Leray- Schauder nonlinear alternative and a fixed-point theorem in cones.
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